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  4. The following figure shows a conducting disc rotating about its axis in a perpendicular magnetic field B . The resistor of resistance R is connected between the centre and the rim. The current in the resistor is (The radius of the disc is 5.0 cm , angular speed ω =10 rad s- 1, B=0.40 T and R=10 Ω ) <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-epmdp35vvaxy.png />

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Q. The following figure shows a conducting disc rotating about its axis in a perpendicular magnetic field $B$ . The resistor of resistance $R$ is connected between the centre and the rim. The current in the resistor is (The radius of the disc is $5.0 \, cm$ , angular speed $\omega =10 \, rad \, s^{- 1}, \, B=0.40 \, T$ and $R=10 \, \Omega $ )

Question

NTA AbhyasNTA Abhyas 2020

Solution:

Emf induced between centre and rim
$\epsilon =\frac{Β \omega a^{2}}{2}, \, wherea=radius$
$\therefore i=\frac{\epsilon }{R}=\frac{B \omega a^{2}}{2 R}=\frac{0.4 \times 10 \times \left(5 \times 1 0^{- 2}\right)^{2}}{2 \times 10}=0.5A$